How do you solve graphically #abs(x – 4)>abs(3x – 1)#?

1 Answer
Lucy
Aug 10, 2018

#-3/2 < x < 5/4#

Explanation:

The first thing you do is to draw the graphs #y=abs(x-4)# and #y=abs(3x-1)# on the SAME graph

graph{(y-abs(x-4))(y-abs(3x-1))=0 [-20.28, 20.27, -10.14, 10.13]}

Now the question is what parts of the graph above satisfies the equation #abs(x-4) > abs (3x-1)#. What it is asking you is what part of the graph #y=abs(x-4)# is above the graph #y=abs(3x-1)#.

Hence, going from the right, the equation of each branch is #y=x-4#, #y=3x-1#, #y=4-x# and #y=1-3x#.

The branches #y=4-x# and #y=3x-1# meet at a point and so do #y=4-x# and #y=1-3x#

Therefore, we need to find the point of intersection

#y=4-x# and #y=3x-1#
#4-x=3x-1#
#5=4x#
#x=5/4#

#y=4-x# and #y=1-3x#
#4-x=1-3x#
#2x=-3#
#x=-3/2#

Finally, looking at where #y=abs(x-4)# is above the graph #y=abs(3x-1)#, we can tell that it is #-3/2 < x < 5/4#

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